Unequal sex ratios and variance in family sizes among mating combinations (sire X dam) can contribute to the effective number of breeders \(N_{b}\) being reduced compared to the potential number of breeders \(N\) contributing to a given spawning event (i.e. brood fish present in spawning tanks).
The maximum effective number of breeders if all pairs (male x female combinations) contribute equally can be calculated as
(Equation. 1)
\[N_{b(max)} =\frac{4(N_{f}N_{m})}{N_{f} + N_{m}}\]
with \(N_{f}\) and \(N_{m}\) denoting the number of females and males potentially contributing to the spawning event, respectively (???).
Generally, some individuals in a spawning tank will not contribute at all; to determine the reduction in \(N_{b}\) due to some individuals not contributing at all the above equation can be used using the number of male and female broodstock that had progeny assigned to them for \(N_{f}\) and \(N_{m}\).
The effect of variance in family size in reducing the effective number of breeders can be calculated as:
(Equation. 2)
\[N_{b} =\frac{4(N_{bf}N_{bm})}{N_{bf} + N_{bm}}\]
With the effective number of females (\(N_{bf}\)) calculated as
(Equation. 3.1)
\[N_{bf}=\frac{1}{\sum_{k=1}^{n_{f}}q_{k}^2}\]
and the effective number of males (\(N_{bf}\)) calculated as
(Equation. 3.2)
\[N_{bf}=\frac{1}{\sum_{k=1}^{n_{f}}q_{k}^2}\]
with \(N_{f}\) and \(N_{m}\) as the actual number of females and and males contributing to a spawning event, and \(q\) as the proportion of progeny contributed by an adult (Lacy 1989Lacy, Robert C. 1989. “Analysis of founder representation in pedigrees: Founder equivalents and founder genome equivalents.” Zoo Biology 8 (2): 111–23. https://doi.org/10.1002/zoo.1430080203.).
Calculate values of maximum attainable \(N_{b}\) given the number of individuals in tanks contributing to a spawning event, and given the actual number of individuals that did have progeny assigned to them. Determine the effective number of breeders based on variance in family size and calculate the reduction in \(N_{b}\) at each sampling point compared to \(N_{b(max)}\) and the reduction due to the fact that some brood fish do not contribute at all.
| E | P | Nm | Nbm | Nf | Nbf | N_tanks | F_tanks | M_tanks | Nb(max) | N_contrib | Nb(max)’ | Nb | Reduct_unsuccessf | Reduct_variance |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| YOY-1 | T1 | 5 | 3.65 | 3 | 2.25 | 10 | 5 | 5 | 10.0 | 8 | 7.50 | 5.56 | 0.25 | 0.44 |
| YOY-1 | T2 | 5 | 4.01 | 3 | 2.28 | 10 | 5 | 5 | 10.0 | 8 | 7.50 | 5.81 | 0.25 | 0.42 |
| YOY-1 | T3 | 5 | 3.71 | 3 | 2.49 | 10 | 5 | 5 | 10.0 | 8 | 7.50 | 5.95 | 0.25 | 0.40 |
| YOY-2 | T1 | 7 | 5.05 | 5 | 3.91 | 20 | 11 | 9 | 19.8 | 12 | 11.67 | 8.82 | 0.41 | 0.55 |
| YOY-2 | T2 | 5 | 3.36 | 4 | 3.11 | 20 | 11 | 9 | 19.8 | 9 | 8.89 | 6.46 | 0.55 | 0.67 |
| YOY-2 | T3 | 7 | 4.27 | 5 | 3.41 | 20 | 11 | 9 | 19.8 | 12 | 11.67 | 7.59 | 0.41 | 0.62 |
| YOY-3 | T1 | 4 | 1.42 | 4 | 1.42 | 15 | 9 | 6 | 14.4 | 8 | 8.00 | 2.84 | 0.44 | 0.80 |
| YOY-3 | T2 | 5 | 2.58 | 4 | 2.55 | 15 | 9 | 6 | 14.4 | 9 | 8.89 | 5.13 | 0.38 | 0.64 |
| YOY-3 | T3 | 5 | 2.65 | 4 | 2.63 | 15 | 9 | 6 | 14.4 | 9 | 8.89 | 5.28 | 0.38 | 0.63 |
Spawning event one, two, and three contained progeny from two, four, and three tanks, respectively. Putatively, each tank contains three females and two males, parentage assignment revealed that one adult assumed to be a female is actually male.
For each spawning event, the expected proportion of progeny assigned per breeder was calculated as the proportion of progeny that should be assigned to a breeder if all breeders of the same sex were to contribute to a spawning event with equal success.
Table 2: Number of males and females per spawning event and expected percent of progeny assigned per breeder if all breeders contribute equally.
| SPAWNING_EVENT | SEX | n | PERC_OFFSP |
|---|---|---|---|
| YOY-1 | F | 5 | 20.00 |
| YOY-1 | M | 5 | 20.00 |
| YOY-2 | F | 11 | 9.09 |
| YOY-2 | M | 9 | 11.11 |
| YOY-3 | F | 9 | 11.11 |
| YOY-3 | M | 6 | 16.67 |
Spawning success of an adult was calculated as the proportion of progeny assigned to a given breeder at the first sampling point (T1) and reproductive success as the proportion of progeny assigned to a given breeder at the final sampling point (T3) when fingerlings were removed to be stocked in the bay.
Table 3a: Proportion of progeny assigned per sire for each time point in pond 1
| sire | T1 | T2 | T3 |
|---|---|---|---|
| ADULT_3160 | 0.400 | 0.277 | 0.258 |
| ADULT_4098 | 0.218 | 0.169 | 0.274 |
| ADULT_4099 | 0.136 | 0.193 | 0.073 |
| ADULT_4154 | 0.027 | 0.036 | 0.048 |
| ADULT_5341 | 0.218 | 0.325 | 0.347 |
Table 3b: Proportion of progeny assigned per dam for each time point in pond 1
| dam | T1 | T2 | T3 |
|---|---|---|---|
| ADULT_4114 | 0.091 | 0.072 | 0.129 |
| ADULT_5123 | 0.564 | 0.506 | 0.379 |
| ADULT_9436 | 0.345 | 0.422 | 0.492 |
Table 3c: Proportion of progeny assigned per pair at stocking.
| dam | sire | n | frq |
|---|---|---|---|
| ADULT_4114 | ADULT_4098 | 12 | 0.10 |
| ADULT_4114 | ADULT_5341 | 4 | 0.03 |
| ADULT_5123 | ADULT_3160 | 32 | 0.26 |
| ADULT_5123 | ADULT_4099 | 9 | 0.07 |
| ADULT_5123 | ADULT_4154 | 6 | 0.05 |
| ADULT_9436 | ADULT_4098 | 22 | 0.18 |
| ADULT_9436 | ADULT_5341 | 39 | 0.31 |
Adults from two spawning tanks contributed to pond 1.
Table 4: Proprtion of expected progeny assigned per breeder if all breeders are equally successful.
| SEX | n | PERC_OFFSP |
|---|---|---|
| F | 5 | 20 |
| M | 5 | 20 |
Compare the difference in observed vs. expected number of progeny assigned to each breeder.
Figure 1: Difference of expected and observed proportion of progeny per male and female and total proportion per parent sent per sampling point (breeders that did not have any progeny assigned are not included in figure).
Compare proportion of progeny assigned to pairs of breeders.
Figure 2: Proportion of progeny assigned to pairs of breeders at each sampling point.
Spawning success of an adult was calculated as the proportion of progeny assigned to a given adult at the first sampling point (T1) and reproductive success as the proportion of progeny assigned to a given breeder at the final sampling point (T3) when fingerlings were removed to be stocked in the bay.
Table 5a: Proportion of progeny assigned per sire for each time point in pond 2.
| sire | T1 | T2 | T3 |
|---|---|---|---|
| ADULT_3160 | 0.212 | 0.077 | 0.102 |
| ADULT_4098 | 0.017 | NA | 0.042 |
| ADULT_4134 | 0.212 | 0.385 | 0.390 |
| ADULT_4136 | 0.110 | 0.026 | 0.144 |
| ADULT_4154 | 0.161 | 0.333 | 0.102 |
| ADULT_5081 | 0.263 | 0.179 | 0.195 |
| ADULT_7514 | 0.025 | NA | 0.025 |
Table 5b: Proportion of progeny assigned per dam for each time point in pond 2.
| dam | T1 | T2 | T3 |
|---|---|---|---|
| ADULT_5123 | 0.042 | NA | 0.068 |
| ADULT_6080 | 0.203 | 0.359 | 0.119 |
| ADULT_7930 | 0.373 | 0.205 | 0.339 |
| ADULT_8155 | 0.169 | 0.051 | 0.085 |
| ADULT_9436 | 0.212 | 0.385 | 0.390 |
Table 5c: Proportion of progeny assigned per pair at stocking.
| dam | sire | n | frq |
|---|---|---|---|
| ADULT_5123 | ADULT_4098 | 5 | 0.04 |
| ADULT_5123 | ADULT_7514 | 3 | 0.03 |
| ADULT_6080 | ADULT_3160 | 3 | 0.03 |
| ADULT_6080 | ADULT_4154 | 11 | 0.09 |
| ADULT_7930 | ADULT_4136 | 17 | 0.14 |
| ADULT_7930 | ADULT_5081 | 23 | 0.19 |
| ADULT_8155 | ADULT_3160 | 9 | 0.08 |
| ADULT_8155 | ADULT_4154 | 1 | 0.01 |
| ADULT_9436 | ADULT_4134 | 46 | 0.39 |
Adults from four spawning tanks contributed to spawning event 2.
Table 6: Proprtion of expected progeny per breeder if all breeders are equally successful.
| SEX | n | PERC_OFFSP |
|---|---|---|
| F | 11 | 9.09 |
| M | 9 | 11.11 |
Compare the difference in observed vs. expected number of progeny assigned to each breeder.
Figure 3: Difference of expected and observed proportion of progeny per male and female and total proportion per parent sent per sampling point (breeders that did not have any progeny assigned are not included in figure).
Compare proportion of progeny assigned to pairs of breeders.
Figure 4: Proportion of progeny assigned to pairs of breeders at each sampling point.
Spawning success of an adult was calculated as the proportion of progeny assigned to a given adult at the first sampling point (T1) and reproductive success as the proportion of progeny assigned to a given breeder at the final sampling point (T3) when fingerlings were removed to be stocked in the bay.
Table 7a: Proportion of progeny assigned per sire for each time point in pond 3.
| sire | T1 | T2 | T3 |
|---|---|---|---|
| ADULT_3160 | NA | 0.010 | NA |
| ADULT_4134 | 0.056 | 0.152 | 0.282 |
| ADULT_4136 | 0.833 | 0.571 | 0.526 |
| ADULT_4154 | 0.037 | 0.095 | 0.038 |
| ADULT_5081 | NA | NA | 0.013 |
| ADULT_8311 | 0.074 | 0.171 | 0.141 |
Table 7b: Proportion of progeny assigned per dam for each time point in pond 3.
| dam | T1 | T2 | T3 |
|---|---|---|---|
| ADULT_4147 | 0.056 | 0.200 | 0.218 |
| ADULT_6080 | 0.037 | 0.105 | 0.038 |
| ADULT_7930 | 0.833 | 0.571 | 0.538 |
| ADULT_9436 | 0.074 | 0.124 | 0.205 |
Table 7c: Proportion of progeny per pair at stocking.
| dam | sire | n | frq |
|---|---|---|---|
| ADULT_4147 | ADULT_4134 | 13 | 0.17 |
| ADULT_4147 | ADULT_8311 | 4 | 0.05 |
| ADULT_6080 | ADULT_4154 | 3 | 0.04 |
| ADULT_7930 | ADULT_4136 | 41 | 0.53 |
| ADULT_7930 | ADULT_5081 | 1 | 0.01 |
| ADULT_9436 | ADULT_4134 | 9 | 0.12 |
| ADULT_9436 | ADULT_8311 | 7 | 0.09 |
Adults from three spawning tanks contributed to spawning event 3.
Table 8: Proprtion of expected progeny per breeder if all breeders are equally successful.
| SEX | n | PERC_OFFSP |
|---|---|---|
| F | 9 | 11.11 |
| M | 6 | 16.67 |
Compare the difference in observed vs. expected number of progeny assigned to each breeder.
Figure 5: Difference of expected and observed proportion of progeny per male and female and total proportion per set of parents per sampling point (breeders that did not have any progeny assigned are not included in figure).
Compare proportion of progeny assigned to pairs of breeders.
Figure 6: Proportion of progeny assigned to pairs of breeders at each sampling point.
Figure 7: Comparison of expected and realized reproductive success per spawning event and sampling point for male and female broodfish
Compare differences by breeder.
Figure 8: Comparison of expected and realized reproductive success per spawning event and sampling point for male and female broodfish that successfully participated in more than one spawning event.
Figure 9: Comparison of proportion of progeny assigned to each family (female x male cross) per spawning event and sampling point.
Table 9a: Mean family size (as proportion of total progeny) per spawning event.
| SPAWNING_EVENT | mean | sd | min | max |
|---|---|---|---|---|
| YOY-1 | 0.143 | 0.113 | 0.024 | 0.400 |
| YOY-2 | 0.125 | 0.119 | 0.008 | 0.390 |
| YOY-3 | 0.150 | 0.223 | 0.010 | 0.833 |
Table 9b: Number of females a male breeds with (putatively three females and two males present in a spawning tank).
| SPAWNING_EVENT | mean female partners |
|---|---|
| YOY-1 | 1.4 |
| YOY-2 | 1.3 |
| YOY-3 | 1.4 |
Table 9c: Number of males a female breeds with (putatively three females and two males present in a spawning tank).
| SPAWNING_EVENT | mean male partners |
|---|---|
| YOY-1 | 2.3 |
| YOY-2 | 1.8 |
| YOY-3 | 1.8 |
The proportion of progeny assigned to breeders at sampling points T1 and T3 was compared to identify differences in spawning and reproductive success among and within breeders.
Figure 10: Comparison of proportion of progeny released per pond assigned to each breeder. Breeders that were in the spawning tanks contributing to a spawning event (SPAWNERS = SP) are denoted as filled circles (YOY1 = yellow, YOY2 = turquoise, YOY3 = purple), even if they did not successfully produce progeny. Breeders that were not in the spawning tanks (SPAWNERS = NOT) for a given spawning event are denoted with an x.
Compare across sampling points
Figure 11: Comparison of proportion of progeny assigned to each broodfish per spawning event and sampling point (T1, blue; T2, green, T3, red). Broodstock that were in the spawning tanks contributing to a spawning event (SPAWNERS = SP) are included, even if they did not successfully produce progeny. Breeders that were not in the spawning tanks (SPAWNERS = NOT) for a given spawning event are denoted with an x.
Total length and weight was determined for adult red drum caught in the wild and introduced to the hatchery as breeders. Condition at introduction was calculated as the weigt/length ratio (measurements in milimeters and grams). The approximate age at introduction to the hatchery was determined using an age-length regression (Porch, Wilson, and Nieland 2002Porch, Clay E., Charles A. Wilson, and David L. Nieland. 2002. “A new growth model for red drum (sciaenops ocellatus) that accommodates seasonal and ontogenic changes in growth rates.” http://aquaticcommons.org/15199/.) which implements a dampend growth model able to account for a decrease in the growth rate over the lifetime of red drum. Approximate age at spawning was determined as the sum of age at introduction and the time spent in the hatchery.
Mean reproductive success at sample points T1 and T3 per breeder was determined as the mean proportion of progeny assigned to an adult across spawning events (adults participated in one to three events).
Figure 13: Spawning and reproductive success per breeder/spawning event.
Table 10: Mean spawning and reproductive success per breeder
| SAMPLE_ID | SEX | AGE_INTROD | TIME_HATCHERY | MEAN_REPROD | STD_REPROD | MEAN_SPAWN | STD_SPAWN | N_EVENTS |
|---|---|---|---|---|---|---|---|---|
| ADULT_4114 | F | 4.8 | 0 | 0.043 | 0.074 | 0.030 | 0.053 | 3 |
| ADULT_4147 | F | 3.9 | 4 | 0.073 | 0.126 | 0.019 | 0.032 | 3 |
| ADULT_4148 | F | 9.6 | 3 | 0.000 | 0.000 | 0.000 | 0.000 | 2 |
| ADULT_4162 | F | 31.7 | 4 | 0.000 | 0.000 | 0.000 | 0.000 | 2 |
| ADULT_5123 | F | 9.6 | 4 | 0.224 | 0.220 | 0.303 | 0.369 | 2 |
| ADULT_6080 | F | 15.0 | 0 | 0.078 | 0.057 | 0.120 | 0.117 | 2 |
| ADULT_7452 | F | 22.9 | 6 | 0.000 | 0.000 | 0.000 | 0.000 | 2 |
| ADULT_777 | F | 12.0 | 6 | 0.000 | 0.000 | 0.000 | 0.000 | 2 |
| ADULT_7930 | F | 15.0 | 6 | 0.438 | 0.141 | 0.603 | 0.325 | 2 |
| ADULT_8155 | F | 15.0 | 4 | 0.042 | 0.060 | 0.084 | 0.120 | 2 |
| ADULT_9436 | F | 20.6 | 5 | 0.362 | 0.145 | 0.210 | 0.136 | 3 |
| ADULT_3160 | M | 16.8 | 4 | 0.120 | 0.130 | 0.204 | 0.200 | 3 |
| ADULT_4098 | M | 8.6 | 3 | 0.158 | 0.164 | 0.118 | 0.142 | 2 |
| ADULT_4099 | M | 12.0 | 2 | 0.036 | 0.052 | 0.068 | 0.096 | 2 |
| ADULT_4134 | M | 3.2 | 5 | 0.336 | 0.076 | 0.134 | 0.110 | 2 |
| ADULT_4136 | M | 7.7 | 5 | 0.335 | 0.270 | 0.472 | 0.511 | 2 |
| ADULT_4154 | M | 3.9 | 4 | 0.063 | 0.034 | 0.075 | 0.075 | 3 |
| ADULT_5081 | M | 9.6 | 0 | 0.104 | 0.129 | 0.132 | 0.186 | 2 |
| ADULT_5341 | M | 12.0 | 5 | 0.347 | 0.000 | 0.218 | 0.000 | 1 |
| ADULT_7514 | M | 18.5 | 0 | 0.025 | 0.000 | 0.025 | 0.000 | 1 |
| ADULT_8311 | M | 3.2 | 0 | 0.070 | 0.100 | 0.037 | 0.052 | 2 |
Spearman Rank correlation coefficient is a rank-based (non-parametric) measure of statistical dependence to assess who well relationship of X and Y can be described using a monotone function i.e. Y either strictly increases (or decreases) as X increases even if that relationship is not linear (Y does not increase by same increment for every increment of X).
Figure 15: Reproductive success at sampling point T1 related to conditioning parameters using each spawning event as an independent observation.
Figure 16: Reproductive success at sampling point T3 related to conditioning parameters using each spawning event as an independent observation.